Polytope of Type {66,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,4}*1584
if this polytope has a name.
Group : SmallGroup(1584,657)
Rank : 3
Schlafli Type : {66,4}
Number of vertices, edges, etc : 198, 396, 12
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   9-fold quotients : {22,4}*176
   11-fold quotients : {6,4}*144
   18-fold quotients : {22,2}*88
   22-fold quotients : {6,4}*72
   36-fold quotients : {11,2}*44
   99-fold quotients : {2,4}*16
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 2.
      7 facets:
         5 of {66}*132
         2 of {33}*66
      99 vertex figures:
         99 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      6 facets:
         6 of {66}*132
      99 vertex figures:
         99 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3.
      8 facets:
         2 of {66}*132
         6 of {22}*44
      66 vertex figures:
         66 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      4 facets:
         4 of {66}*132
      66 vertex figures:
         66 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 6.
      5 facets:
         3 of {22}*44
         2 of {33}*66
      33 vertex figures:
         33 of {4}*8

Permutation Representation (GAP) :

s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,23)(13,33)(14,32)(15,31)(16,30)(17,29)(18,28)(19,27)(20,26)(21,25)(22,24)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68)(45,89)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,78)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79);;
s1 := ( 1,35)( 2,34)( 3,44)( 4,43)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,46)(13,45)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,57)(24,56)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(67,68)(69,77)(70,76)(71,75)(72,74)(78,79)(80,88)(81,87)(82,86)(83,85)(89,90)(91,99)(92,98)(93,97)(94,96);;
s2 := (12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,67)(24,68)(25,69)(26,70)(27,71)(28,72)(29,73)(30,74)(31,75)(32,76)(33,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(99)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,23)(13,33)(14,32)(15,31)(16,30)(17,29)(18,28)(19,27)(20,26)(21,25)(22,24)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68)(45,89)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,78)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79);
s1 := Sym(99)!( 1,35)( 2,34)( 3,44)( 4,43)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,46)(13,45)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,57)(24,56)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(67,68)(69,77)(70,76)(71,75)(72,74)(78,79)(80,88)(81,87)(82,86)(83,85)(89,90)(91,99)(92,98)(93,97)(94,96);
s2 := Sym(99)!(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,67)(24,68)(25,69)(26,70)(27,71)(28,72)(29,73)(30,74)(31,75)(32,76)(33,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);
poly := sub<Sym(99)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2 >;

References : None.
to this polytope

Polytope of Type {66,4}

Twisty Puzzle